Nonrelativistic Perpendicular Shocks Modeling Young Supernova Remnants: Nonstationary Dynamics and Particle Acceleration at Forward and Reverse Shocks

Abstract

For parameters that are applicable to the conditions at young supernova remnants, we present results of twodimensional, three-vector (2D3V)particle-in-cell simulations of a non-relativistic plasma shock with a large-scale perpendicular magnetic field inclined at a  45 angle to the simulation plane to approximate three-dimensional (3D) physics. We developed an improved clean setup that uses the collision of two plasma slabs with different densities and velocities, leading to the development of two distinctive shocks and a contact discontinuity. The shock formation is mediated by Weibel-type filamentation instabilities that generate magnetic turbulence. Cyclic reformation is observed in both shocks with similar period, for which we note global variations due to shock rippling and local variations arising from turbulent current filaments. The shock rippling occurs on spatial and temporal scales produced by the gyro-motions of shock-reflected ions. The drift motion of electrons and ions is not a gradient drift, but is commensurate withÉ B drift. We observe a stable supra-thermal tail in the ion spectra, but no electron acceleration because the amplitude of the Buneman modes in the shock foot is insufficient for trapping relativistic electrons. We see no evidence of turbulent reconnection. A comparison with other twodimensional (2D) simulation results suggests that the plasma beta and the ion-to-electron mass ratio are not decisive for efficient electron acceleration, but the pre-acceleration efficacy might be reduced with respect to the 2D results once 3D effects are fully accounted for. Other microphysical factors may also play a part in limiting the amplitude of the Buneman waves or preventing the return of electrons to the foot region.

Electron Pre-acceleration at Nonrelativistic High-Mach-number Perpendicular Shocks

“…Our choice of Alfvénic Mach numbers, M 30 A  , should therefore in all cases lead to the formation of shocks with strong electrostatic Buneman waves in the foot region. However, we note that even a moderate variation in the simulation parameters (e.g., M A , p b , magnetic-field configuration) may introduce significantly different results: from the absence of a nonthermal population (Wieland et al 2016) to a large nonthermal fraction produced by the Buneman instability and adiabatic heating (Matsumoto et al 2012). Here we investigate the impact of the magnetic-field configuration; namely, the angle between the regular magnetic field and the simulation plane.…”

“…As the magnetic field is assumed to be frozen in the moving plasma, a motional electric field E v B = -´is also initialized in the left and right beam, = -, the motional electric field has opposing signs in the two slabs. To avoid an artificial electromagnetic transient resulting from this strong gradient in the motional electric field when the two plasma beams start to interact, we use a modified flow-flow method of shock excitation, recently developed by us and described in Wieland et al (2016). This method implements a transition zone between the plasma beams, in which the electromagnetic fields are tapered off until they vanish in a small plasma-free area that initially separates the beams.…”

“…Multiple rapid interactions of electrons with electrostatic waves in the foot region of a shock give rise to SSA and produce suprathermal tails in the electron spectra. 2D simulations of SSA at perpendicular shocks have been discussed in a number of papers (e.g., Amano & Hoshino 2009a;Matsumoto et al 2012Matsumoto et al , 2013Wieland et al 2016). The trajectories of accelerated electrons in multidimensional systems are more complicated than in 1D, but the process is still referred to as SSA.…”

“…To explore electron energization via SSA, the Alfvénic Mach number, M A , should satisfy a threshold condition for the excitation of electrostatic waves in the shock foot (Matsumoto et al 2012). The thermal velocity of the electrons should be smaller than the relative speed between incoming electrons and reflected ions, leading to (Wieland et al 2016 is the density ratio of reflected to incoming ions. Note that the ion temperature, T i , is measured far upstream, whereas the electron temperature, T e , is local, because the threshold condition involves the local thermal speed of electrons.…”

“…Early 1D simulations (Quest 1985;Lembege & Dawson 1987) and recent 2D simulations (Umeda et al 2008(Umeda et al , 2009(Umeda et al , 2014Wieland et al 2016) indicated that supercritical perpendicular shocks become nonstationary and undergo cyclic self-reformation. Therefore, all instabilities driven by reflected ions in the foot region will also evolve in a nonstationary way, and the conditions for the Buneman-wave growth and efficient SSA will probably be met only at certain locations and time periods.…”